Is there any possibility in any field theory model that at coupling >= 1.0, perturbation theory can be used to calculate, say field propagators beyond tree level? What is the room left for perturbation theory in this situation? In other words, is perturbation relevant at all at the above mentioned couplings?
Asked
Active
Viewed 135 times
1 Answers
1
Yes it is still relevant in some sense. An analogy is the expansion of $(1-g)^{-1}$ as a formal power series $\sum_{k=0} g^k$ for $g>1$. Truncating the power series is not itself useful as an approximation since each next order term gets larger and larger. But we can use methods such as Borel summation to recover the exact result $(1-g)^{-1}$ from the formal power series, so information about the exact result is still hidden in the power series even though the power series is not practically useful as an approximation method.
From a theoretical point of view the real problem with the perturbative expansion is that it misses corrections going schematically like $\sim e^{-1/g}$ which are often important in the exact result. This problem has nothing to do with the magnitude of $g$ per se.
octonion
- 9,072